Mathematical instrument



Oct. 1, 1940. GRAHAM I 2,216,172

MATHEMATI CAL INSTRUMENT Filed Nov. 18. 1938 WWW/E 0 INVENTOR. fie'zia/w firakafi B gig/47M 11.

JA ATTORNEY.

Patented Oct. 1, 1940 UNITED, STATES PATENT OFFICE MATHEMATIUAL INSTRUMENT Frederic L. Graham, New York, N. Y. Application November 18, 1938, Serial No. 241,175 11 Claims. (01. 33-45) This invention relates to mathematical instruments and is herein disclosed in some detail as embodied in a navigating device in the form of a velocity trianglegraph and flight calculator '6 suitable for airplane pilots.

One of the serious problems facing pilots arises from the need to allow for the force and direction of the wind. According to the present invention the necessary corrections can be arrived at by mechanical operations which give a direct numerical reading to the person manipulating them without any computingwhatever;

In one form the device enables the pilot to mechanically ascertain the force and direction of the wind if he can observe the track and ground speed, andthus avoid all the time and attention and knowledge'needed to solve the socalled triangle of velocities.

The instrument of the present invention is adapted to be easily held in the hand, requires no pencil or other temporary-marking, and is completely self-contained. Moreovenit is rugged in constructiomcapable of being cheaply built,

requires no mental arithmetic and has few moving parts.

Other features and advantages will hereinafter appear.

In the accompanying drawing,

Figure l is a face of an instrument embodying the invention, parts, being partly broken away,

and, some rulings only partly, shown.

Figure 2 is a sectional view on the broken line 22 of Figure 1.

In the form shown,,the instrument includes a 85 built up body 3 having in effect a rabbeted central circle cut out of it so that the ledge 4 of the rabbet accommodates the projecting annular edge 5 of built up annular azimuth circle. In which is graduated in degrees or aliquot numbers of degrees.

The azimuth circle It also includes an internal annular projection ii, in which lies the external rabbet 1 of a built up disc l3 forming a wind grid ruled in two directions at right angles to each other. In the form shown alternate ruled lines are broken lines, thus facilitating rapid following by the eye.

On a pivot I 5 at one sideof the body 3 are shown four pointers l4, l6, l1, [8 which extend across the faces of the wind grid l3 and azimuth circle II], and are prolonged so as to catch under an arcuate overhang 8.

In the form shown two of the pointers l4 and I6 are so curved adjacent the pivot l5 that their facing edges form radii from the pivot l5, and.

are graduated in distances that approximate to the spaced rulings on the wind grid. The other two pointers l1 and I8 similarily form a pair with edges so curved that their facing edges form radii from the pivot l5 and are identically grad- 5* uated.

The overhang holds each pair of pointers down at their outer ends so that they cannot pass each other, and the pointers are graduated and V numbered to represent the first digits of speeds lb or distances in units of ten miles each, counting the pivot l5 as zero.

The overhang 8 is shown as graduated uniformly so that when an even tendegree unit of the azimuth circle is set centrally (at the central 15 mark on the overhang) each fifth successive unit on the overhang 8 is at the end of a connecting straight line drawn from the successive ten degree marking on the azimuth circle, with the result that the temporary position of a pointer I4, 20

l6, I! or I8 may be temporarily identified by reading on the azimuth circle the number in degrees pointed out by the opposite end of its connecting straight line;

In the form shown the sine, and other trigog nometrical functions, of any angle at the pivot 15, are proportionately equal to the functions of the angle subtended from the center of the wind grid.

The construction thus summarized enables a 36* pilot torapidly find the flight course and the distance flown given, the true course and distance, and the force and direction of the wind.

For example, the true magnetic course being from the magnetic meridian, ground dis- 35 tance miles, the wind blowing 25 miles an hour at 45, and the air speed of the airplane being 90 miles an hour, to find the course and distance to be flown, the azimuth circle I0 is rotated until one of the aliquot degree marks on 40 the circle, say the degree mark 8 (standing for 80) coincides with one of the continued lines I l which join the outer semi-circle [2. The outer semi-circle [2 then becomes a field on which magnetic bearings will be indicated, because each 45 continued line i I joints some aliquot degree mark on the circle [0 :to' the outer semi-circle I2.

In Figure 1, this brings the azimuth circle or course mark It) so that it is joined by a continued linetothe graduation line Am the outer 50 semi-circle l2.

Then the wind grid I3 is rotated until the arrow on it points directly away from the wind direction. i i r Next the pointer I4 is swung on its pivot l5 to 55' bring its arrow-head to the point A. Then pointer I B on the same pivot I5 is swung until the graduation line 9 on it, representing a speed of 90 miles an hour, is at a ruled broken wind line which extends two and one-half spaces from the pointer Hi to the pointer I 4 (these two and one-half spaces representing 25 miles per hour).

Now the arrow on pointer l6 shows the flight course to be steered, the directional reading being found by following the corresponding line H down to the number shown on the azimuth circle.

The air of flight distance also may be read by starting from the graduation l8 (representing 180 miles) on pointer l4 and following from this graduation l8 along the wind line on the wind grid to where the wind line intersects with pointer it, giving a reading on the pointer l6 of 223 miles (the 22.3 actually read representing 223 miles). The angle between the pointers l4 and I6 representing the drift angle.

To solve another problem such as the duble drift angle known as the wind star problem, four pointers are required. In this problem the pilot is seeking to learn the direction and strength of the wind, based on the conditions assumed in the previous example.

. For example, while steering a course of 86 off the magnetic north, the drift angle is observed to be 14 to the right. On altering the course 26 into'the wind (to the left) and steering a course of 60, the drift angle is observed to be 6 to the right. Airspeed is known to be 90 miles per hour. To find force and direction of the wind, the

. azimuth circle is again set with 8 at the central perpendicular line. Pointer I6 is set to the first course 86, read on the azimuth circle, as in the previous example, the pointer M is then set 14 to the right thereof which turns out to be the point on the outer semi-circle I2 connected to the 100 (shown as 10) on the azimuth 10.

The pointer I! is then set to the second course 60, and the pointer 18 is set at an angle 6 to the right of pointer I! or 66. The wind grid is then rotated until the length of the wind line between the pointers l4 and I6 is the same length as the wind line between pointers H and [8, starting in each case from the known airspeed 90 miles per hour, indicated on pointers l6 and H.

The arrow on the wind grid then points toward or away from the wind.

It wlil be noted that the built up body and disc and annular azimuth are each built of three layers 2|, 22 and 23 of Celluloid and that the pivot l and hubs of the pointers are covered by an overlying sheet 20 of Celluloid.

It will be seen that the overhang 8 and shield 20 are each spaced from the sheet or layer 2| by a layer 25 of Celluloid and that the edge 26 of the body 3 is smoothed oiT by a Celluloid cement filling 21 at the center, and that the shield 20 is bent down on each side of the pivot to be fiat on the body 3 beyond the limit of swing of the pointers.

Having thus described one embodiment of the invention what is claimed is:

1. A calculating device including a body, a ruled disc rotatable in the body, a graduated annular disc rotatable between the ruled disc and the body and supporting the ruled disc, and a pair of separately settable pointers pivoted outside the discs on the body and graduated to correspond with the rulings on the disc and adapted to swing eccentrically across the discs.

2. A calculating device including a body, a

ruled disc rotatable in the body, a graduated annular disc rotatable between the ruled disc and the body and supporting the ruled disc, a pair of separately settable pointers pivoted outside the discs on the body and graduated to correspond with the rulings on the disc and adapted to swing eccentrically across the discs, and a graduated arc across which the pointers swing connected by lines to coincide with the graduated spaces on theannular disc.

3. A calculating device including a body, a ruled disc rotatable in the body, a graduated annular disc rotatable between the ruled disc and the body and supporting the ruled disc, a 'pair of separately settable pointers pivoted outside the discs on the body and graduated to correspond with the rulings on the disc and adapted to swing eccentrically across the discs, and a second pair of pointers similarly graduated and pivoted to swing across another area of the discs.

4. A calculating device including a body, a ruled disc rotatable in the body, a graduated annular disc rotatable between the ruled disc and the body and supporting the ruled disc, a pivot in the body outside the discs, and a pair of separately settable pointers pivoted on the pivot and having each a straight edge radial to the pivot and graduated to correspond with rulings on the disc and swinging eccentrically over it so that they point to graduations on the body.

5. A calculating device including a body, a ruled disc rotatable in the body, a graduated annular disc rotatable between the ruled disc and the body and supporting the ruled disc, a pivot in the body outside the discs, a pair of separately settable pointers pivoted on the pivot and having each a straight edge radial to the pivot and graduated to correspond with rulings on the disc and swinging eccentrically over it so that they point to graduations on the body, and a second pair of separately settable pointers each having a straight edge radial to the pivot and graduated to correspond with the rulings on the disc and pointing to graduations on the body.

6. A calculating device including a body, a

ruled disc rotatable in the body, a graduated annular disc rotatable between the ruled disc and the body and supporting the ruled disc, a pivot in the body outside the discs, a pair of separately settable pointers pivoted on the pivot and having each a straight edge radial to the pivot and graduated to correspond with rulings on the disc and swinging eccentrically over it, and a graduated arc across which the pointers swing and having its graduations connected by lines to coincide with the graduated spaces on the annular disc.

'7. A calculating device including a body, a ruled disc rotatable in the body, a graduated annular disc rotatable between the ruled disc and the body and supporting the ruled disc, a pivot in the body outside the discs, a pair of separately settable pointers pivoted on the pivot and having each a straight edge radial to the pivot and graduated to correspond with rulings on the disc and swinging eccentrically over it, a second pair of separately settable pointers each having a straight edge radial to the same pivot and graduated to correspond with the rulings on the disc, and a graduated arc across which the pointers swing and having its graduations connected by lines to coincide with the graduated spaces on the annular disc.

8. A calculating device including a body, a ruled disc rotatable in the body, and ruled in squares,

a graduateed annular disc rotatable between the ruled disc and the body and graduated in degrees and supporting the ruled disc, a pivot in the body outside the discs, and a pair of separately settable pointers pivoted on the pivot and having each a straight edge radial to the pivot and graduated to correspond with rulings on the disc and swinging eccentrically over it and pointing to graduations on the body.

9. A calculating device including a body, a ruled disc rotatable in the body, and ruled in squares, a graduated annular disc rotatable between the ruled disc and the body and graduated in degrees and supporting the ruled disc, a pivot in the body outside the discs, a pair of separately settable pointers pivoted on the pivot and having each a straight edge radial to the pivot and graduated to correspond with rulings on the disc and swinging eccentrically over it and pointing to graduations on the body, and a second pair of separately settable pointers each having a straight edge radial to the same pivot and graduated to correspond with the rulings on the disc and pointing to graduations on the body.

10. A calculating device including a body, a ruled disc rotatable in the body, and ruled in squares, a graduated annular disc rotatable between the ruled disc and the body and graduated in degrees and supporting the ruled disc, a pivot in the body outside the discs, a pair of pointers pivoted on the pivot and having each a straight edge radial to the pivot and graduated to correspond with rulings on the disc and swinging eccentrically over it, and a graduated arc across which the pointers swing connected by lines to coincide with the graduated spaces on the annular disc.

11. A calculator having a three layer body, a three layer annular degree measuring rotatable ring within the body, a three layer disc within the ring, pointers pivoted above the body, a shield overlying the base of the pointers, a Celluloid spacer for the shield, and a cement filler smoothing off the edge of the shield.

FREDERIC L. GRAHAM. 

